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首页> 外文期刊>The Journal of Chemical Physics >Computing the non-Markovian coarse-grained interactions derived from the Mori-Zwanzig formalism in molecular systems: Application to polymer melts
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Computing the non-Markovian coarse-grained interactions derived from the Mori-Zwanzig formalism in molecular systems: Application to polymer melts

机译：计算来自Mori-Zwanzig形式主义的非马利维亚粗粒相互作用：在聚合物熔体中的应用

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摘要

Memory effects are often introduced during coarse-graining of a complex dynamical system. In particular, a generalized Langevin equation (GLE) for the coarse-grained (CG) system arises in the context of Mori-Zwanzig formalism. Upon a pairwise decomposition, GLE can be reformulated into its pairwise version, i.e., non-Markovian dissipative particle dynamics (DPD). GLE models the dynamics of a single coarse particle, while DPD considers the dynamics of many interacting CG particles, with both CG systems governed by non-Markovian interactions. We compare two different methods for the practical implementation of the non-Markovian interactions in GLE and DPD systems. More specifically, a direct evaluation of the non-Markovian (NM) terms is performed in LE-NM and DPD-NM models, which requires the storage of historical information that significantly increases computational complexity. Alternatively, we use a few auxiliary variables in LE-AUX and DPD-AUX models to replace the non-Markovian dynamics with a Markovian dynamics in a higher dimensional space, leading to a much reduced memory footprint and computational cost. In our numerical benchmarks, the GLE and non-Markovian DPD models are constructed from molecular dynamics (MD) simulations of star-polymer melts. Results show that a Markovian dynamics with auxiliary variables successfully generates equivalent non-Markovian dynamics consistent with the reference MD system, while maintaining a tractable computational cost. Also, transient subdiffusion of the star-polymers observed in the MD system can be reproduced by the coarse-grained models. The non-interacting particle models, LE-NM/AUX, are computationally much cheaper than the interacting particle models, DPD-NM/AUX. However, the pairwise models with momentum conservation are more appropriate for correctly reproducing the long-time hydrodynamics characterised by an algebraic decay in the velocity autocorrelation function. Published by AIP Publishing.
机译：在复杂动态系统的粗晶中通常引入记忆效应。特别地，在森夸齐格形式主义的背景下，粗粒（CG）系统的广义Langevin等式（GLE）产生了森林的范围。在成对分解时，GLE可以重新格式化到其成对版本中，即非马尔可夫耗散粒子动力学（DPD）。 GLE模拟单个粗粒粒子的动态，而DPD则考虑许多交互CG粒子的动态，其中CG系统由非马尔可夫互动控制。我们比较了两种不同的方法，以实现GLE和DPD系统中的非马尔可夫交互的实际实施。更具体地，在LE-NM和DPD-NM模型中执行非马尔可夫（NM）术语的直接评估，该模型需要存储显着提高计算复杂性的历史信息。或者，我们在Le-Aux和DPD-AUX模型中使用一些辅助变量，以用更高的维度空间中的马尔科维亚动态替换非马尔可夫动态，导致更大的内存占用和计算成本。在我们的数控基准中，GLE和非马尔可夫DPD模型由星聚合物熔体的分子动力学（MD）模拟构成。结果表明，具有辅助变量的马尔可夫动态成功地生成了与参考MD系统一致的等效非Markovian Dynamics，同时保持了易解的计算成本。而且，在MD系统中观察到的星聚合物的瞬态苯偏见可以通过粗粒模型再现。非交互粒子模型LE-NM / AUX比交互粒子模型，DPD-NM / AUX便宜得多。然而，具有动量守恒的成对模型更适合于正确地再现具有在速度自相关函数中的代数衰减的长时间流体动力学。通过AIP发布发布。

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